Development of fuzzy $$ \bar{X} - S $$ control charts with unbalanced fuzzy data

Abstract

Statistical process control is an effective quality control technique to monitor a production process with balanced data under certain conditions. However, there are some situations where dealing with uncertainty and unbalanced data is considered. In such situations, the traditional statistical control charts are not effective to obtain control limits. The aim of this paper is fourfold. First of all, the collected unbalanced data are converted to triangular fuzzy numbers for each sample. Second, this paper develops a fuzzy $$ \bar{X} - S $$ control chart while dealing with unbalanced fuzzy data. Third, a proposed approach is presented on how to deal with unbalanced fuzzy data for calculations of control limits. Besides, fuzzy process capability analyses are conducted to measure process performance. Finally, an illustrative example is conducted to show the effectiveness of the proposed fuzzy $$ \bar{X} - S $$ control chart with unbalanced data for uncertainty.